30 research outputs found
INSTABILITY OF A NIELSEN-OLESEN VORTEX EMBEDDED IN THE ELECTROWEAK THEORY: II. ELECTROWEAK VORTICES AND GAUGE EQUIVALENCE
Vortex configurations in the electroweak gauge theory are investigated. Two
gauge-inequivalent solutions of the field equations, the Z and W vortices, have
previously been found. They correspond to embeddings of the abelian
Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown
here that any electroweak vortex solution can be mapped into a solution of the
same energy with a vanishing upper component of the Higgs field. The
correspondence is a gauge equivalence for all vortex solutions except those for
which the winding numbers of the upper and lower Higgs components add to zero.
This class of solutions, which includes the W vortex, instead corresponds to a
singular solution in the one-component gauge. The results, combined with
numerical investigations, provide an argument against the existence of other
vortex solutions in the gauge-Higgs sector of the Standard Model.Comment: 6 pages, plain latex, no figures, submitted to Mod. Phys. Lett. A as
"Electroweak Vortices and Gauge Equivalence"
Vortex Dynamics in Dissipative Systems
We derive the exact equation of motion for a vortex in two- and three-
dimensional non-relativistic systems governed by the Ginzburg-Landau equation
with complex coefficients. The velocity is given in terms of local gradients of
the magnitude and phase of the complex field and is exact also for arbitrarily
small inter-vortex distances. The results for vortices in a superfluid or a
superconductor are recovered.Comment: revtex, 5 pages, 1 encapsulated postscript figure (included), uses
aps.sty, epsf.te
as the Topological Origin of B+L Violation in the Hot Electroweak Theory
The space of static finite-energy configurations in the electroweak theory
admits a topological structure. More precisely, we show that this space
contains two disconnected sectors of unstable gauge-Higgs fields odd under a
properly defined generalized parity. This classification extends the
description of baryon and lepton number violating electroweak processes to the
symmetric phase of the theory. Configurations with odd pure-gauge behaviour at
spatial infinity, such as the sphaleron, multisphalerons, electroweak strings
as well as an infinite surface of their equivalents, have half-integer
Chern-Simons number and mediate B+L violating processes in the early universe.
Finite-energy configurations with even pure-gauge behaviour, such as the
new sphaleron and electroweak strings, are topologically equivalent to the
vacuum and are irrelevant for B+L violation. We discuss the possible formation
of B+L violating quark-lepton condensates in the symmetric high-temperature
phase of the electroweak theory.Comment: LaTeX, 30 pages, 4 encapsulated postscript figures (included,
uuencoded), uses epsf.tex. Title/references modified, minor stylistic change
Electroweak Origin of Cosmological Magnetic Fields
Magnetic fields may have been generated in the electroweak phase transition
through spontaneous symmetry breaking or through the subsequent dynamical
evolution of semiclassical field configurations. Here I demonstrate explicitly
how magnetic fields emerge spontaneously in the phase transition also when no
gradients of the Higgs field are present. Using a simple model, I show that no
magnetic fields are generated, at least initially, from classical two-bubble
collisions in a first-order phase transition. An improved gauge-invariant
definition of the electromagnetic field is advocated which is more appropriate
in the sense that it never allows electrically neutral fields to serve as
sources for the electromagnetic field. In particular, semiclassical
configurations of the Z field alone do not generate magnetic fields. The
possible generation of magnetic fields in the decay of unstable Z-strings is
discussed.Comment: Revtex, 36 pages, uses aps.sty. Version accepted for publication.
Includes estimates of strength and correlation length of the magnetic field
for each mechanism of generation. Conclusion about two-bubble collisions
weakened. Higgs current clarified. References added. Title shortene